Answers
The angles 1 and 5 have the same measure, since they are corresponding angles.
Then:
[tex]m\angle5=123^{\circ}[/tex]The angles 5 and 6 are supplementary angles, this means that their measures add up to 180°. Then:
[tex]\begin{gathered} m\angle5+m\angle6=180 \\ \Rightarrow123+m\angle6=180 \end{gathered}[/tex]Substract 123 from both sides of the equation:
[tex]\begin{gathered} m\angle6=180-123 \\ =57 \end{gathered}[/tex]Therefore, the measure of the angle 6 is 57°.
Related Questions
What transformations produce the graph of g(x)=5^-x+2 from the graph of the parent function f(x)=5^x? Select all that apply.
Answers
Solution
For this case we have the following function:
[tex]g(x)=5^{-x+2}[/tex]And we want to find the steps to obtain the above function from this one:
[tex]f(x)=5^x^{}[/tex]So we can do the following:
Reflection over the x axis
horizontal shift to the left 2 units
Calculate the mass of silver 6.0 ml of silver with a density of 10.5G/ml
Answers
Let's use the formula about density.
[tex]\rho=\frac{m}{V}[/tex]Let's use the given magnitudes. The density is 10.5 g/mL but we need to approximate it to the whole number, and the volume is 6.0 mL.
[tex]11(\frac{g}{mL})=\frac{m}{6.0mL}[/tex]We have to multiply each side by 6.0 to find the mass.
[tex]\begin{gathered} 11(\frac{g}{mL})\cdot6=\frac{m}{6.0mL}\cdot6 \\ m=66g \end{gathered}[/tex]Therefore, the mass is 66 grams.Find the x- and y- intercept of each linear equation.b) y = 3x + 9
Answers
Answer:
The x and y intercepts for y = 3x + 9 are:
y-intercept: 9
x-intercept: -3
Step-by-step explanation:
I only see one equation: y = 3x + 9
This is in the slope-intercept format of y=mx + b, where m is the slope and b the y-intercept (the value of y when x = 0).
This means the y-intercept is 9. When x = o, y = 9.
The x-intercept is the point the line crosses the x avis, so y = 0. Use y = 0 in the equation and calculate the value of x:
y=3x+9
0=3x+9
3x= -9
x = -3
See the attached graph.
At a town fair, everyone who wins one of the contests selects a prize. There are 14 prizes available, including 7 pies, 4 gift certificates, 2 fruit baskets, and 1 bicycle. (Suppose all prizes are equally valuable to each conestant.)
What is the probability that the first 3 winners will all select gift certificates?
What is the probability that the first winner will select either a pie or a fruit basket?
Answers
Problem 1
A = probability 1st winner picks gift certificate (no replacement)
A = 4/14 = 2/7
B = probability 2nd winner picks gift certificate (no replacement)
B = 3/13
C = probability 3rd winner picks gift certificate (no replacement)
C = 2/12 = 1/6
D = probability first 3 winners pick gift certificate (no replacement)
D = A*B*C
D = (2/7)*(3/13)*(1/6)
D = (2*3*1)/(7*13*6)
D = 6/546
D = 1/91 is the final answer
======================================================
Problem 2
A = probability 1st winner picks pie
A = 7/14
B = probability 1st winner picks fruit basket
B = 2/14
C = probability 1st winner picks pie OR fruit basket
C = A+B
C = 7/14 + 2/14
C = 9/14 is the final answer
what the square roof of 500
Answers
We want to know the square root of 500
[tex]\sqrt[]{500}[/tex]To find it, we have to factor 500
500 | 2
250 | 2
125 | 5
25 |
What is the sum of the arithmetic series 3 + 12 +21+...+597?
Answers
The sum of the arithmetic series is 20,100.
What is Arithmetic series?
The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: in Formula 1 If Sn denotes the sum of a term-filled arithmetic sequence, then The first and last term values, as well as the total number of terms, are necessary for this formula.
We can use the below formula to find the sum of arithmetic series,
[tex]s_n = \frac{n(a_1 + a_n)}{2}[/tex]
In this example [tex]a_1 = 3, a_n = 597[/tex]
First we have to find the value of n.
To find n, use the formula for an arithmetic sequence [tex]a_n = a_1 + (n-1)d[/tex]
where d is the common difference between the terms (found by subtracting a previous term from a term).
In this example, d = 12 - 3 = 9.
To find n, plug [tex]a_n = 597, a_1 = 3, d = 9[/tex] into [tex]a_n = a_1 + (n-1)d[/tex]
[tex]597 = 3 + (n - 1)9\\597 = 3 + 9n - 9\\597 = 9n - 6\\603 = 9n\\n = 67[/tex]
Now plug, [tex]n = 67, a_1 = 3, a_n = 597[/tex] into [tex]s_n = \frac{n(a_1 + a_n)}{2}[/tex]
[tex]S_n = \frac{67(3 + 597)}{2}\\ S_n = \frac{40200}{2} \\S_n = 20100[/tex]
Therefore, the sum of the given arithmetic series is, 20100.
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(x-9)(×+4)=168 solve for xI just need reminded how to do the x-9 * x+4 please
Answers
The given expression is
[tex](x-9)(x+4)=168[/tex]To solve the product, we have to use the distributive property
[tex]x^2+4x-9x-36=168[/tex]Then, we move all the terms to the left side to combine like terms
[tex]\begin{gathered} x^2+4x-9x-36-168=0 \\ x^2-5x-204=0 \end{gathered}[/tex]Now, we use the quadratic formula to find the solutions
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a = 1, b = -5, and c = -204. Let's replace these values
[tex]\begin{gathered} x_{1,2}=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(1)(-204)}}{2(1)} \\ x_{1,2}=\frac{5\pm\sqrt[]{25+816}}{2}=\frac{5\pm\sqrt[]{841}}{2} \\ x_{1,2}=\frac{5\pm29}{2} \end{gathered}[/tex]There are two solutions
[tex]\begin{gathered} x_1=\frac{5+29}{2}=\frac{34}{2}=17 \\ x_2=\frac{5-29}{2}=\frac{-24}{2}=-12 \end{gathered}[/tex]Hence, the solutions are x = 17, and x = -12.6. Give the detailed steps you would take to enter the following equation in your graphingcalculator. Then provide a table of values using the table feature of your graphingcalculator.2x + y = 4
Answers
We have to solve this equation:
[tex]2x+y=4[/tex]We have two variables and one equation that is linear.
We can make a table by giving values to x and then calculating the corresponding value of y.
Then, first we have to clear y from the equation.
We can do this as:
[tex]\begin{gathered} 2x+y=4 \\ y=4-2x \end{gathered}[/tex]Then, we can calculate 3 points to make a table of values.
In a calculator, we have to press the keys '4', '-', '2', 'x' and the value we assigned to x.
For example if we start with x = 0, we would press: 4, -, 2, x, 0, = and obtain the value of y that correspond to x = 0.
We than can complete the table as:
x | y
-----|------
0 | 4
1 | 2
2 | 0
We can assign another values to x and obtain new values of y.
DISTRIBUTE
6(-4-9x)
SOLVE AND SHOW WORK
Answers
The simplified value after distributive property is -24 - 9x.
What is Distributive Property?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
a × (b + c) = (a × b) + (a × c).
given:
6(-4-9x)
Using Distributive property
a x( b+ c) = ax b + a x c
So, 6(-4-9x)
= 6 x (-4) + 6 x (-9x)
= -24 - 9x
Hence, 6(-4-9x)= -24 - 9x
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whats the scale dilation
Answers
Answer:
1/2
Step-by-step explanation:
Given a figure showing dilation of LMNO to give L'M'NO', you want to know the scale factor.
Scale factorThe scale factor of a dilation is the ratio of dilated lengths to original lengths. We can choose any of the lengths in the figure to find the dilation scale factor.
scale factor = M'N/MN = 3/6
scale factor = 1/2
A homeowner in New jersey needs to build a square garden for her tomato plants this spring. She figures she needs an area of 49 square feet. What are the dimensions of her garden?
Answers
She needs an area of 49 square feet.
The garden has a square form, so we find the side length with the following formula.
[tex]\begin{gathered} s=\sqrt[]{A} \\ s=\sqrt[]{49ft^2} \\ s=7ft \end{gathered}[/tex]The side length is 7 feet.
Therefore, the dimensions are 7 feet by 7 feet.The length of the longer leg of a right triangle is 13 m more than three times the length of the shorter leg. The length of the hypotenuse is 14 m more than three times the length of the shorter leg. Find the side lengths of the triangle.
Answers
SOLUTION:
Step 1 :
Set up the right triangle with the following:
side a = x
side b = 13 + 3x
side c = 14 + 3x
Using pythagorean theorem :
[tex]a^2+b^2=c^2[/tex][tex]x^2+(13+3x)^2=(14+3x)^2[/tex]Step 2 :
Expand this equation by using foil to get:
[tex]x^2+(169+78x+9x^2)=196+84x+9x^2[/tex]
Simplifying this equation will give you:
[tex]x^2\text{ - 6 x - 27 = 0}[/tex]
Step 3 :
Factor this to get:
(x-9)(x +3) = 0
Solving this will give you x = 9 or x = -3.
The side length cannot be negative so discard the -3.
Step 4 :
Your side lengths will be:
[tex]\begin{gathered} a\text{ = x = 9 m} \\ b\text{ = 13 + 3 x = 13 + 3 ( 9 ) = 13 + 27 = 40 m} \\ \text{c = 14 + 3 x = 14 + 3 ( 9 ) = 14 + 27 = 41 m} \end{gathered}[/tex]CONCLUSION:
The side lengths of the triangle are:
9 m , 40 m and 41 m
Please help me with this….
Answers
Answer:
Step-by-step explanation:
Number 1) The answer is [tex]5\sqrt{3} \\[/tex] and [tex]-5\sqrt{3}[/tex]
Number 2) The answer is no solution
Number 3) The answer is [tex]-3\sqrt{3}[/tex] and [tex]3\sqrt{3}[/tex]
Find the Domain and Range. There are four different answer choices, A, B, C, & D; which one is the correct answer choice?
Answers
For the graphed function we have:
Domain: (-4, ∞)Range: [0, ∞)So the correct option is D.
Which is the domain and range of the graphed function?
For a function y = f(x), the domain is the set of the possible inputs, this is the possible values of x that we can use in the function.
To identify the domain on a graph, we need to look at the horizontal axis.
To find the minimum of the domain we look at the leftmost value, in this case it is x = -4 marked with a open circle, which means that the value itself does not belong to the domain, so we write this end as (-4,
To find the maximum we look at the right side, here we can see that we have an arrow that points to the right, so the function keeps going to the right, then the domain is:
D: (-4, ∞)
The range is the set of the y-values, so this time we look at the vertical axis.
The minimum is the lowest value, in this case, is y = 0.
The maximum is the top most value, in this case, we can see that the arrow points upwards, then we don't have a maximum, the range is:
R: [0, ∞)
The correct option is D.
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How many different ID cards can be made if there are three digits on a car in no digit can be used more than once? What if digits can be repeated?
Answers
Explanation
The question wants us to determine the number of different ID cards that can be made if there are 3 digits on a car.
To do so, let us first list out all the possible outcomes. These are:
[tex]0,1,2,3,4,5,6,7,8,9[/tex]We can see that there are 10 possible digits
For the first case where no digit can be used more than once, we will have
Therefore, there are
[tex]10\times9\times8=720\text{ ID cards}[/tex]For the second case, if the digits can be repeated, then, we will have
Then, since the numbers can be repeated, we will have
[tex]10\times10\times10=1000\text{ ID cards}[/tex]Please find the volume worth 60 points
Answers
The volume of the figure is 3, 718 cubic units
How to determine the volumeIt is important to note that the formula for determining the volume of a right rectangular prism is expressed as;
V = whl
Where;
v is the volume of the rectangular prismw is the width of the rectangular prismh is the height of the rectangular prisml is the length of the rectangular prismNow, we have the dimensions as;
Height = 8 + 18 = 26 units
Width = 11 units
length = 13 units
Substitute the values
Volume = 11 × 1 3× 26
Volume = 3, 718 cubic units
Hence, the value is 3, 718 cubic units
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Hello how do I find The measure of side a
Answers
Solution:
To figure out the value of a, we will use the trigonometric ratio below
[tex]\begin{gathered} sin\theta=\frac{a}{c} \\ \theta=41^0 \\ c=25m \\ sin\theta=\frac{opposite}{hypotenus} \\ S=\frac{O}{H} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} s\imaginaryI n\theta=\frac{a}{c} \\ \sin41=\frac{a}{25m} \\ a=25\times sin41 \\ a=16.4 \\ a\approx16cm \end{gathered}[/tex]Hence,
The value of a to the nearest whole number is
[tex]a=16m[/tex]directions on a box of five cups of wallpaper paste are to mix the contents with four quarts of water. to mix a smaller batch using one cup of paste how much water and ounces should be added note that one quart equals 32 oz
Answers
5 cups------128 oz
1 cup--------128/5 oz
to mix one cup of wallpaper paste we will need to add 25.6 oz of water
Write an algebraic expression that models the given situation.
2 more than the product of -7 and a number, x
Answers
Answer:
-7x + 2
Step-by-step explanation:
I believe this is the answer. When I see the word "than" I work backwards. So -7 times x plus 2.
Which of the following is another way to express the 6^5(6*6*6)*66*(6 *6 *6) *66*6*6*6*6* 6(6 * 6) + (6 + 6 + 6)
Answers
we have the following:
[tex]undefined[/tex]
As a club fundraiser,
of students washed 40 cars
one weekend. The next
weekend, they washed 70
cars. What was the percent
increase in the number of
cars washed? how do i set up the problem??
Answers
Answer:
[tex]\frac{70 - 40}{40}*100[/tex]
Step-by-step explanation:
Use the percent increase formula:
The final value is 70, because that's what they end with.
The initial value is 40, because that's what they start with.
Percent Increase = [tex]\frac{Final Value - Initial Value }{Initial Value} *100%[/tex]
write the fraction 1 1/4 as a decimal
Answers
Answer:
1.25
Step-by-step explanation:
Step 1: Multiply the whole number by the denominator
1 x 4 = 4
Step 2: Add the result of step 1 to the numerator
4 + 1 = 5
Step 3: Divide the result of step 2 by the denominator
5 ÷ 4 = 1.25
The function f(x) is graphed below. What is true about the graph on the intervalfrom point c to point d?baeSubmit AnsweroIt is positive and increasingaIt is positive and decreasingIt is negative and increasingIt is negative and decreasing
Answers
The graph of f(x) shown is a wave form.
From the interval from point c to point d, the graph falls on the negative y-axis and slopes downwards.
Therefore, f(x) is negative and decreasing from point c to point d on the graph.
point H is a centroid. RS = 7.5, TV = 11, and WR = 6. Find the missing segment lengths
Answers
Applying the definition of the centroid, the missing segment lengths are:
TU = 5.5
TR = 15
VU = 5.5
RV = 12
VW = 6
TS = 7.5
What is the Centroid of a Triangle?A centroid is the point where all the three medians that each divide the three sides of a triangle intersect each other. This means that, the medians joins the vertex of a triangle to the midpoint of the side of the triangle that is directly opposite it.
Given that point H is the centroid of triangle RTV, it means that the three medians of triangle RTV intersect at point H, and divides each of the sides of the triangle into equal segments.
Given the following lengths:
RS = 7.5TV = 11WR = 6Based on the knowledge of the centroid of a triangle, we have;
TU = 1/2(TV)
Substitute
TU = 1/2(11)
TU = 5.5
TR = 2(RS)
Substitute
TR = 2(7.5)
TR = 15
VU = 1/2(TV)
Substitute
VU = 1/2(11)
VU = 5.5
RV = 2(WR)
Substitute
RV = 2(6)
RV = 12
VW = WR
Substitute
VW = 6
TS = RS
Substitute
TS = 7.5
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a reporter for an international newspaper is given an assignment that is randomly chosen from the following destinations worldwide: 10 continental united states assignments, 18 south american assignments, 20 european union assignments, and 14 asian assignments. find the probability that he gets an assignment in the united states or asia. express your answer as a fraction
Answers
Given:
10 continental united states assignments
18 south american assignments
20 european union assignments
14 asian assignments
All possible outcome =10+18+20+14 =62
Required outcome is 10 or 14
[tex]\text{Probability}=\frac{required\text{ outcome}}{\text{all possible outcome}}[/tex][tex]P(\text{getting assignment in united state or asia)=}\frac{10}{62}+\frac{14}{62}[/tex][tex]\begin{gathered} =\frac{24}{62} \\ \\ =\frac{12}{31} \end{gathered}[/tex]Which expression is equivalent to ½ sin 2 theta for all values of theta
Answers
Given:
Given the expression
[tex]\frac{1}{2}\sin2\theta[/tex]Required: An equivalent expression
Explanation:
Use the formula
[tex]\sin2\theta=2\sin\theta\cos\theta[/tex]Dividing by 2 on both sides gives
[tex]\begin{gathered} \frac{1}{2}\sin2\theta=\frac{1}{2}(2\sin\theta\cos\theta) \\ =\sin\theta\cos\theta \end{gathered}[/tex]Option D is correct.
Final Answer: An equivalent expression of
[tex]\frac{1}{2}\sin2\theta[/tex]is
[tex]\cos\theta\sin\theta[/tex]Shawna's Bikes rents bikes for $19 plus $4 per hour. Lea paid $39 to rent a bike. For how many hours did she rent the bike?
Answers
Answer: Lea rented the bike for 5 hours.
{(2,2),(2,5),(2,1),(2,7),(2,-1).(2,-4)) is a function. O True O False
Answers
This is not a function since by definition x values can only have one image on y, and we see that in this case it has a l,ot of images on y:
x
(2, 2) (2, 5) (2, 1)
Solve the inequality in express your answer in interval notation used decimal form for numerical values
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given inequality
[tex]-12<3z-9\leq18[/tex]STEP 2: Simplify the inequality
[tex]\begin{gathered} -12\lt3z-9\leq18 \\ \mathrm{If}\:a-1 \end{gathered}[/tex]Solve the other part
[tex]\begin{gathered} 3z-9\leq18 \\ 3z\leq18+9 \\ 3z\leq27 \\ z\leq\frac{27}{3}=9 \\ z\leq9 \end{gathered}[/tex]STEP 3: Combine the intervals
[tex]z>-1\quad \mathrm{and}\quad \:z\le \:9[/tex]STEP 4: Merge the overlapping intervals
[tex]-1STEP 5: Give the answer in interval notationHence, the final answer will be given as:
[tex](-1,9][/tex]What is the product of the expressions? (3x +5/y6)(4y3/5
Answers
Given:
Given the product
[tex](\frac{3x+5}{y^6})(\frac{4y^3}{5})[/tex]